Two-Particle Scattering on Non-Translation Invariant Line Lattices

Abstract

Quantum walks have been used to develop quantum algorithms since their inception, and can be seen as an alternative to the usual circuit model; combining single-particle quantum walks on sparse graphs with two-particle scattering on a line lattice is sufficient to perform universal quantum computation. In this work we solve the problem of two-particle scattering on the line lattice for a family of interactions without translation invariance, recovering the Bose-Hubbard interaction as the limiting case. Due to its generality, our systematic approach lays the groundwork to solve the more general problem of multi-particle scattering on general graphs, which in turn can enable design of different or simpler quantum gates and gadgets. As a consequence of this work, we show that a CPHASE gate can be achieved with high fidelity when the interaction acts only on a small portion of the line graph.

14 pages, 4 figures

References in corpus (7)

• Universal computation by quantum walk
• Exponential algorithmic speedup by quantum walk
• Universal computation by multi-particle quantum walk
• Two-particle states in the Hubbard model
• A passive CPHASE gate via cross-Kerr nonlinearities
• Two photons co- and counter-propagating through $N$ cross-Kerr sites
• Levinson's theorem for graphs II

Cited by in corpus (2)

• Two-particle scattering on general graphs
• Photon-Number Conserved Universal Quantum Logic Employing Continuous-Time Quantum Walk on Dual-Rail Qubit Arrays